As Cayley graphs have a lot of properties which are desirable in an interconnection network, such as vertex transitivity, edge transitivity, hierarchical structure, high fault tolerance, many researchers have proposed Cayley graphs as models for interconnection networks [1]}. Let \(\mathcal {A}\)  be a finite group and \(\Omega \)  be a subset of \(\mathcal {A}\) , where the identity of the group does not belong to \(\Omega \) . The Cayley graph \({\rm Cay}(\mathcal {A}, \Omega )\)  is a digraph with vertex set \(\mathcal {A}\)  and arc set \(\lbrace (a, a\cdot \omega )| a\in \mathcal {A}, \omega \in \Omega \rbrace \) . If \(\Omega =\Omega ^{-1}\) , then \({\rm Cay}(\mathcal {A}, \Omega )\)  is an undirected graph, where \(\Omega ^{-1}=\lbrace \omega ^{-1}| \omega \in \Omega \rbrace \) .
